**Balbharati Solutions Class 6 Mathematics HCF LCM**

Welcome to NCTB Solutions. Here with this post we are going to help 6th class students for the Solutions of Balbharati Class 6 Mathematics Book, Practice Set 23, 24 and 25, HCF LCM. Here students can easily find step by step solutions of all the problems for HCF LCM. Also our Expert Mathematic Teacher’s solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get HCF LCM solutions. Here all the solutions are based on Maharashtra State Board latest syllabus.

**HCF LCM all Question Solutions :**

**Practice Set 23** :

**Question no – (1) **

**Solution : **

**(1)** Given, numbers are 12, 16

Factors of 12 = 1, 2, 3, 4, 6, 12

Factors of 16 = 1, 2, 4, 8, 16

Common Factors = 1, 2, 4

**(2) **Given, numbers are 21, 24

Factors of 21 = 1, 3, 7, 21

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24

Common Factors of both number is 1 and 3

**(3) **Given, numbers are 25, 30.

Factors of 25 = 1, 5, 25

Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30

Common Factors of both number is 1 and 5.

**(4) **Given, numbers are 24, 25.

Factors of 24 = 1, 2, 3, 4, 6, 8, 12, 24

Factors of 25 = 1, 5, 25

Common Factor = 1

**(5)** Given, numbers are 56, 72.

Factors of 56 is = 1, 2, 4, 7, 8, 14, 28, 56

Factors of 72 is = 1, 2, 3, 4, 6, 8, 9, 18, 24, 36, 72

Common Factors of both number are 1, 2, 4, 8.

**Practice Set 24** :

**Question no – (1) **

**Solution : **

**(1) To find factor of 45 and 30.**

Factors of 45 = 1, 3, 5, 9, 15, 45

Factors of 30 = 1, 2, 3, 5, 6, 10, 15, 30

Common factors = 1, 3, 5, 15

Thus, HCF ( 45 and 30) = 15

**(2) To find factor of 16 and 48**

Factors of 16 = 1,2, 4, 8, 16

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Common factors = 1, 2, 4, 8, 16

Thus, the HCF of 16 and 48 is 16

**(3) To find factor of 39 and 25.**

Factors of 39 is = 1, 3,13, 39

Factors of 25 is = 1, 5, 25

Common factor of both the number is 1

Thus, the HCF of 39 and 25 is = 1

**(4) To find factor of 49 and 56**

Factors of 49 = 1, 7 , 49

Factors of 56 = 1, 2, 4, 7, 8, 14, 28 , 56

Common factors of both number is 1, 7

Thus, the HCF of 49 and 56 is 1, 7

**(5) To find factor of 120, 144.**

Factors of 120 is = 1 , 2, 3, 4, 5, 12 , 24 , 30, 60, 120

Factors of 144 is = 1, 2, 3, 4, 12, 24, 76, 144

Common factors of both the numbers are = 1, 2, 3, 4, 12, 24

Thus, the HCF of 120 and 144 is = 24

**(6) To find factor of 81 and 99**

Factors of 81 = 1, 3, 9, 27, 81

Factors of 99 = 1, 3, 9, 11, 33, 99

Common factors of both the numbers = 1,3, 9

Thus, HCF ( 81,99) = 9

**(7) To find factor of 24, 36**

Factors of 24 is = 1, 2, 3, 4, 6, 8, 12, 24

Factors of 36 is = 1, 2,3, 4, 6, 9, 12, 18, 36

Common factors of the both number is = 1, 2, 3, 4 , 6 , 12

Hence, the HCF of 24 and 36 = 12

**(8) To find factor of 25 and 75**

Factors of 25 is = 1, 5, 25

Factors of 75 is = 1, 5, 15, 25, 75

Common factors for both the number is = 1, 5, 25

Hence, the HCF of 25 and 75 is = 25

**(9) To find factor of 48, 54**

Factors of 48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

Factors of 54 : 1, 2,3, 6, 9, 18, 27, 54

Common factors of both the number are 1, 2, 3, 6,

∴ The HCF of 48 and 54 is 6.

**(10) To find factor of 150, 225**

Factors of 150 is = 1,2, 3, 5, 6, 10, 15, 25, 30, 75, 150

Factors of 225 is = 1, 3, 5, 15, 25, 75, 225

Common factors of both the number is = 1, 3, 5, 15, 25, 75

Thus, the HCF of 150 and 225 is = 75.

**Question no – (2) **

**Solution : **

We required to find HCF of 18 and 15

Factors of 18 is = 1, 2, 3, 9, 18

Factors of 15 is = 1, 3, 5, 15

Common factors of both the number is = 1,3

Thus, the HCF of 18 and 15 = 3

Hence, the maximum length of each bed is 3 meters.

**Practice Set 25**:

**Question no – (1) **

**Solution : **

**(1) 9 and 15.**

9 time table = 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

15 time table = 15, 30, 45, 60, 75

Since, lowest common multiple is 45

**∴ ** The LCM of 9 and 15 = 45

**(2) 2, 3 and 5.**

2 time table is = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30

3 time table is = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30

5 time table is = 5, 10, 15, 20, 25, 30, 35, 40

Since, lowest common multiple is 30

Hence, The LCM of 2,3 and 5 is 30.

**(3) 12 and 28**

12 time table = 12, 24, 36, 48, 60, 72, 84, 96, 108, 120

28 time table = 28, 56, 84, 112, 140

Since, lowest common multiple is 84

The LCM of 12 and 28 = 84.

**(4) 15, 20**

15 time table is = 15, 30, 45, 60, 75, 90, 105, 120, 135, 150

20 time table is = 20, 40, 60, 80

Since, lowest common multiple is 60

Therefore, the LCM of 15 and 20 = 60

**(5) 8 and 11.**

8 time table is = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96

11 time table is = 11, 22, 33, 44, 55, 66, 77, 88, 99

Since, the lowest common multiple is 88

The LCM of 8 and 11 is = 88.

**Question no – (2) **

**Solution : **

**(1)** We required to find LCM of 20 and 25.

20 time table is = 20,40,60,80,100,120,140

25 time table is = 25, 50, 75, 100, 125

Since, The lowest common multiple is 100

Therefore, the LCM of 20 and 25 = 100

**(2)** We required to find LCM of 16, 24, and 40.

16 time table is = 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240

24 time table is = 24, 48, 72, 96, 120, 144, 168, 192, 216, 240

40 time table is = 40, 80, 120, 160, 200, 240

Since, lowest common multiple is 240.

Hence, the LCM of 16, 24 and 40 = 240

**(4)** We required to find LCM of 60, 120 and 24

60 time table is = 60, 120, 180

120 time table is = 120, 240,360

24 time table is = 24, 48, 72, 96,120, 144

Since, lowest common multiple is 120.

Therefore, the LCM of 60, 120 and 24 is = 120

**(5)** Given the fractions 13/45 and 22/ 75

We required to find LCM of 45 and 75.

45 time table is = 45, 90, 135, 180, 225, 270, 315

75 time table is = 75, 150, 225, 300

Since, the lowest common multiple is 225.

Thus, the LCM of 45 and 75 = 225

Therefore,

13 × 5/45 × 5 = 65/225 ….. (Eqn.1)

22×3/75×3 =66 /225 …. (Eqn. 2)

Adding Eqn. 1 and 2

65/225 + 66/225 = 131/225

**More Solutions : **

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